Bessel Functions - 10.68 Modulus and Phase Functions

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
10.68#Ex5	${\displaystyle{\displaystyle M_{\nu}\left(x\right)=({\operatorname{ber}_{\nu}^{2}}x+{\operatorname{bei}_{\nu}^{2}}x)^{\ifrac{1}{2}}}}$ \HankelmodM{\nu}@{x} = (\Kelvinber{\nu}^{2}@@{x}+\Kelvinbei{\nu}^{2}@@{x})^{\ifrac{1}{2}}	${\displaystyle{\displaystyle\Re(\nu+k+1)>0}}$	Error	Sqrt[KelvinBer[\[Nu], x]^2 + KelvinBei[\[Nu], x]^2] == ((KelvinBer[\[Nu], x])^(2)+ (KelvinBei[\[Nu], x])^(2))^(Divide[1,2])	Missing Macro Error	Successful	-	Successful [Tested: 30]
10.68#Ex6	${\displaystyle{\displaystyle N_{\nu}\left(x\right)=({\operatorname{ker}_{\nu}^{2}}x+{\operatorname{kei}_{\nu}^{2}}x)^{\ifrac{1}{2}}}}$ \HankelmodderivN{\nu}@{x} = (\Kelvinker{\nu}^{2}@@{x}+\Kelvinkei{\nu}^{2}@@{x})^{\ifrac{1}{2}}		Error	Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2] == ((KelvinKer[\[Nu], x])^(2)+ (KelvinKei[\[Nu], x])^(2))^(Divide[1,2])	Missing Macro Error	Successful	-	Successful [Tested: 30]
10.68#Ex9	${\displaystyle{\displaystyle M_{-n}\left(x\right)=M_{n}\left(x\right)}}$ \HankelmodM{-n}@{x} = \HankelmodM{n}@{x}		Error	Sqrt[KelvinBer[- n, x]^2 + KelvinBei[- n, x]^2] == Sqrt[KelvinBer[n, x]^2 + KelvinBei[n, x]^2]	Missing Macro Error	Failure	-	Successful [Tested: 9]
10.68#Ex17	${\displaystyle{\displaystyle N_{-\nu}\left(x\right)=N_{\nu}\left(x\right)}}$ \HankelmodderivN{-\nu}@{x} = \HankelmodderivN{\nu}@{x}		Error	Sqrt[KelvinKer[- \[Nu], x]^2 + KelvinKei[- \[Nu], x]^2] == Sqrt[KelvinKer[\[Nu], x]^2 + KelvinKei[\[Nu], x]^2]	Missing Macro Error	Failure	-	Successful [Tested: 30]